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70-603: In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields . The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules . Electromagnetism can be thought of as a combination of electrostatics and magnetism , which are distinct but closely intertwined phenomena. Electromagnetic forces occur between any two charged particles. Electric forces cause an attraction between particles with opposite charges and repulsion between particles with

140-492: A Dirac delta function susceptibility χ (Δ t ) = χδ (Δ t ) . It is convenient to take the Fourier transform with respect to time and write this relationship as a function of frequency. Because of the convolution theorem , the integral becomes a simple product, This frequency dependence of the susceptibility leads to frequency dependence of the permittivity. The shape of the susceptibility with respect to frequency characterizes

210-487: A car accident , or even objects as big as the stars of a galaxy . Another type, microscopic particles usually refers to particles of sizes ranging from atoms to molecules , such as carbon dioxide , nanoparticles , and colloidal particles . These particles are studied in chemistry , as well as atomic and molecular physics . The smallest particles are the subatomic particles , which refer to particles smaller than atoms. These would include particles such as

280-469: A granular material . Permittivity In electromagnetism , the absolute permittivity , often simply called permittivity and denoted by the Greek letter ε ( epsilon ), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in

350-436: A nonlinear medium , the permittivity can depend on the strength of the electric field. Permittivity as a function of frequency can take on real or complex values. In SI units, permittivity is measured in farads per meter (F/m or A ·s ·kg ·m ). The displacement field D is measured in units of coulombs per square meter (C/m ), while the electric field E is measured in volts per meter (V/m). D and E describe

420-407: A capacitor is based on its design and architecture, meaning it will not change with charging and discharging. The formula for capacitance in a parallel plate capacitor is written as where A {\displaystyle A} is the area of one plate, d {\displaystyle d} is the distance between the plates, and ε {\displaystyle \varepsilon }

490-567: A dimensionless quantity (relative permeability) whose value in vacuum is unity . As a consequence, the square of the speed of light appears explicitly in some of the equations interrelating quantities in this system. Formulas for physical laws of electromagnetism (such as Maxwell's equations ) need to be adjusted depending on what system of units one uses. This is because there is no one-to-one correspondence between electromagnetic units in SI and those in CGS, as

560-413: A force law for the interaction between elements of electric current, Ampère placed the subject on a solid mathematical foundation. A theory of electromagnetism, known as classical electromagnetism , was developed by several physicists during the period between 1820 and 1873, when James Clerk Maxwell 's treatise was published, which unified previous developments into a single theory, proposing that light

630-410: A homogeneous material is usually given relative to that of free space, as a relative permittivity ε r (also called dielectric constant , although this term is deprecated and sometimes only refers to the static, zero-frequency relative permittivity). In an anisotropic material, the relative permittivity may be a tensor, causing birefringence . The actual permittivity is then calculated by multiplying

700-435: A link between human-made electric current and magnetism was Gian Romagnosi , who in 1802 noticed that connecting a wire across a voltaic pile deflected a nearby compass needle. However, the effect did not become widely known until 1820, when Ørsted performed a similar experiment. Ørsted's work influenced Ampère to conduct further experiments, which eventually gave rise to a new area of physics: electrodynamics. By determining

770-474: A magnetic field transforms to a field with a nonzero electric component and conversely, a moving electric field transforms to a nonzero magnetic component, thus firmly showing that the phenomena are two sides of the same coin. Hence the term "electromagnetism". (For more information, see Classical electromagnetism and special relativity and Covariant formulation of classical electromagnetism .) Today few problems in electromagnetism remain unsolved. These include:

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840-445: A magnetic needle using a Voltaic pile. The factual setup of the experiment is not completely clear, nor if current flowed across the needle or not. An account of the discovery was published in 1802 in an Italian newspaper, but it was largely overlooked by the contemporary scientific community, because Romagnosi seemingly did not belong to this community. An earlier (1735), and often neglected, connection between electricity and magnetism

910-581: A medium is related to its relative permittivity ε r by So in the case of a vacuum, The susceptibility is also related to the polarizability of individual particles in the medium by the Clausius-Mossotti relation . The electric displacement D is related to the polarization density P by The permittivity ε and permeability µ of a medium together determine the phase velocity v = ⁠ c / n ⁠ of electromagnetic radiation through that medium: The capacitance of

980-429: A medium to static electric fields is described by the low-frequency limit of permittivity, also called the static permittivity ε s (also ε DC ): At the high-frequency limit (meaning optical frequencies), the complex permittivity is commonly referred to as ε ∞ (or sometimes ε opt ). At the plasma frequency and below, dielectrics behave as ideal metals, with electron gas behavior. The static permittivity

1050-450: A nearby compass needle to move. At the time of discovery, Ørsted did not suggest any satisfactory explanation of the phenomenon, nor did he try to represent the phenomenon in a mathematical framework. However, three months later he began more intensive investigations. Soon thereafter he published his findings, proving that an electric current produces a magnetic field as it flows through a wire. The CGS unit of magnetic induction ( oersted )

1120-437: A perfect vacuum has a relative permittivity of exactly 1 whereas at standard temperature and pressure , air has a relative permittivity of ε r air ≡ κ air ≈ 1.0006 . Relative permittivity is directly related to electric susceptibility ( χ ) by otherwise written as The term "permittivity" was introduced in the 1880s by Oliver Heaviside to complement Thomson 's (1872) " permeability ". Formerly written as p ,

1190-492: A role in chemical reactivity; such relationships are studied in spin chemistry . Electromagnetism also plays several crucial roles in modern technology : electrical energy production, transformation and distribution; light, heat, and sound production and detection; fiber optic and wireless communication; sensors; computation; electrolysis; electroplating; and mechanical motors and actuators. Electromagnetism has been studied since ancient times. Many ancient civilizations, including

1260-410: A sewing-needle by means of the discharge of Leyden jars." The electromagnetic force is the second strongest of the four known fundamental forces and has unlimited range. All other forces, known as non-fundamental forces . (e.g., friction , contact forces) are derived from the four fundamental forces. At high energy, the weak force and electromagnetic force are unified as a single interaction called

1330-507: A unified concept of energy. This unification, which was observed by Michael Faraday , extended by James Clerk Maxwell , and partially reformulated by Oliver Heaviside and Heinrich Hertz , is one of the key accomplishments of 19th-century mathematical physics . It has had far-reaching consequences, one of which was the understanding of the nature of light . Unlike what was proposed by the electromagnetic theory of that time, light and other electromagnetic waves are at present seen as taking

1400-550: Is where The constants c and µ o were both defined in SI units to have exact numerical values until the 2019 revision of the SI . Therefore, until that date, ε o could be also stated exactly as a fraction,   1 c 2 μ 0 = 1 35 950 207 149.472 7056 π  F/m   {\displaystyle \ {\tfrac {1}{c^{2}\mu _{0}}}={\tfrac {1}{35\,950\,207\,149.472\,7056\pi }}{\text{ F/m}}\ } even if

1470-497: Is farad per meter (F/m). The permittivity is often represented by the relative permittivity ε r which is the ratio of the absolute permittivity ε and the vacuum permittivity ε 0 This dimensionless quantity is also often and ambiguously referred to as the permittivity . Another common term encountered for both absolute and relative permittivity is the dielectric constant which has been deprecated in physics and engineering as well as in chemistry. By definition,

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1540-413: Is a good approximation for alternating fields of low frequencies, and as the frequency increases a measurable phase difference δ emerges between D and E . The frequency at which the phase shift becomes noticeable depends on temperature and the details of the medium. For moderate field strength ( E o ), D and E remain proportional, and Since the response of materials to alternating fields

1610-451: Is characterized by a complex permittivity, it is natural to separate its real and imaginary parts, which is done by convention in the following way: where The choice of sign for time-dependence, e , dictates the sign convention for the imaginary part of permittivity. The signs used here correspond to those commonly used in physics, whereas for the engineering convention one should reverse all imaginary quantities. The complex permittivity

1680-411: Is compatible with special relativity. According to Maxwell's equations, the speed of light in vacuum is a universal constant that is dependent only on the electrical permittivity and magnetic permeability of free space . This violates Galilean invariance , a long-standing cornerstone of classical mechanics. One way to reconcile the two theories (electromagnetism and classical mechanics) is to assume

1750-467: Is especially useful when modelling nature , as the full treatment of many phenomena can be complex and also involve difficult computation. It can be used to make simplifying assumptions concerning the processes involved. Francis Sears and Mark Zemansky , in University Physics , give the example of calculating the landing location and speed of a baseball thrown in the air. They gradually strip

1820-399: Is named in honor of his contributions to the field of electromagnetism. His findings resulted in intensive research throughout the scientific community in electrodynamics. They influenced French physicist André-Marie Ampère 's developments of a single mathematical form to represent the magnetic forces between current-carrying conductors. Ørsted's discovery also represented a major step toward

1890-450: Is rather general in meaning, and is refined as needed by various scientific fields. Anything that is composed of particles may be referred to as being particulate. However, the noun particulate is most frequently used to refer to pollutants in the Earth's atmosphere , which are a suspension of unconnected particles, rather than a connected particle aggregation . The concept of particles

1960-474: Is studied, for example, in the subject of magnetohydrodynamics , which combines Maxwell theory with the Navier–Stokes equations . Another branch of electromagnetism dealing with nonlinearity is nonlinear optics . Here is a list of common units related to electromagnetism: In the electromagnetic CGS system, electric current is a fundamental quantity defined via Ampère's law and takes the permeability as

2030-547: Is the case for mechanical units. Furthermore, within CGS, there are several plausible choices of electromagnetic units, leading to different unit "sub-systems", including Gaussian , "ESU", "EMU", and Heaviside–Lorentz . Among these choices, Gaussian units are the most common today, and in fact the phrase "CGS units" is often used to refer specifically to CGS-Gaussian units . The study of electromagnetism informs electric circuits , magnetic circuits , and semiconductor devices ' construction. Particles The term particle

2100-468: Is the net electric flux passing through the surface, Q enc {\displaystyle Q_{\text{enc}}} is the charge enclosed in the Gaussian surface, E {\displaystyle \mathbf {E} } is the electric field vector at a given point on the surface, and d A {\displaystyle \mathrm {d} \mathbf {A} } is a differential area vector on

2170-420: Is the permittivity of the medium between the two plates. For a capacitor with relative permittivity κ {\displaystyle \kappa } , it can be said that Permittivity is connected to electric flux (and by extension electric field) through Gauss's law . Gauss's law states that for a closed Gaussian surface , S , where Φ E {\displaystyle \Phi _{E}}

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2240-587: The Greeks and the Mayans , created wide-ranging theories to explain lightning , static electricity , and the attraction between magnetized pieces of iron ore . However, it was not until the late 18th century that scientists began to develop a mathematical basis for understanding the nature of electromagnetic interactions. In the 18th and 19th centuries, prominent scientists and mathematicians such as Coulomb , Gauss and Faraday developed namesake laws which helped to explain

2310-424: The chemical and physical phenomena observed in daily life. The electrostatic attraction between atomic nuclei and their electrons holds atoms together. Electric forces also allow different atoms to combine into molecules, including the macromolecules such as proteins that form the basis of life . Meanwhile, magnetic interactions between the spin and angular momentum magnetic moments of electrons also play

2380-411: The dispersion properties of the material. Moreover, the fact that the polarization can only depend on the electric field at previous times (i.e. effectively χ (Δ t ) = 0 for Δ t < 0 ), a consequence of causality , imposes Kramers–Kronig constraints on the susceptibility χ (0) . As opposed to the response of a vacuum, the response of normal materials to external fields generally depends on

2450-539: The electron or a helium-4 nucleus . The lifetime of stable particles can be either infinite or large enough to hinder attempts to observe such decays. In the latter case, those particles are called " observationally stable ". In general, a particle decays from a high- energy state to a lower-energy state by emitting some form of radiation , such as the emission of photons . In computational physics , N -body simulations (also called N -particle simulations) are simulations of dynamical systems of particles under

2520-563: The electroweak interaction . Most of the forces involved in interactions between atoms are explained by electromagnetic forces between electrically charged atomic nuclei and electrons . The electromagnetic force is also involved in all forms of chemical phenomena . Electromagnetism explains how materials carry momentum despite being composed of individual particles and empty space. The forces we experience when "pushing" or "pulling" ordinary material objects result from intermolecular forces between individual molecules in our bodies and in

2590-562: The frequency of the field. This frequency dependence reflects the fact that a material's polarization does not change instantaneously when an electric field is applied. The response must always be causal (arising after the applied field), which can be represented by a phase difference. For this reason, permittivity is often treated as a complex function of the (angular) frequency ω of the applied field: (since complex numbers allow specification of magnitude and phase). The definition of permittivity therefore becomes where The response of

2660-632: The particle in a box model, including wave–particle duality , and whether particles can be considered distinct or identical is an important question in many situations. Particles can also be classified according to composition. Composite particles refer to particles that have composition – that is particles which are made of other particles. For example, a carbon-14 atom is made of six protons, eight neutrons, and six electrons. By contrast, elementary particles (also called fundamental particles ) refer to particles that are not made of other particles. According to our current understanding of

2730-595: The quantized nature of matter. In QED, changes in the electromagnetic field are expressed in terms of discrete excitations, particles known as photons , the quanta of light. Investigation into electromagnetic phenomena began about 5,000 years ago. There is evidence that the ancient Chinese , Mayan , and potentially even Egyptian civilizations knew that the naturally magnetic mineral magnetite had attractive properties, and many incorporated it into their art and architecture. Ancient people were also aware of lightning and static electricity , although they had no idea of

2800-444: The Gaussian surface. If the Gaussian surface uniformly encloses an insulated, symmetrical charge arrangement, the formula can be simplified to where   θ   {\displaystyle \ \theta \ } represents the angle between the electric field lines and the normal (perpendicular) to S . If all of the electric field lines cross the surface at 90°, the formula can be further simplified to Because

2870-451: The ability to disturb a compass needle. The link between lightning and electricity was not confirmed until Benjamin Franklin 's proposed experiments in 1752 were conducted on 10   May 1752 by Thomas-François Dalibard of France using a 40-foot-tall (12 m) iron rod instead of a kite and he successfully extracted electrical sparks from a cloud. One of the first to discover and publish

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2940-725: The baseball of most of its properties, by first idealizing it as a rigid smooth sphere , then by neglecting rotation , buoyancy and friction , ultimately reducing the problem to the ballistics of a classical point particle . The treatment of large numbers of particles is the realm of statistical physics . The term "particle" is usually applied differently to three classes of sizes. The term macroscopic particle , usually refers to particles much larger than atoms and molecules . These are usually abstracted as point-like particles , even though they have volumes, shapes, structures, and etc. Examples of macroscopic particles would include powder , dust , sand , pieces of debris during

3010-474: The components of a colloid. A colloid is a substance microscopically dispersed evenly throughout another substance. Such colloidal system can be solid , liquid , or gaseous ; as well as continuous or dispersed. The dispersed-phase particles have a diameter of between approximately 5 and 200 nanometers . Soluble particles smaller than this will form a solution as opposed to a colloid. Colloidal systems (also called colloidal solutions or colloidal suspensions) are

3080-404: The constituents of atoms – protons , neutrons , and electrons – as well as other types of particles which can only be produced in particle accelerators or cosmic rays . These particles are studied in particle physics . Because of their extremely small size, the study of microscopic and subatomic particles falls in the realm of quantum mechanics . They will exhibit phenomena demonstrated in

3150-501: The deep connections between electricity and magnetism that would be discovered over 2,000 years later. Despite all this investigation, ancient civilizations had no understanding of the mathematical basis of electromagnetism, and often analyzed its impacts through the lens of religion rather than science (lightning, for instance, was considered to be a creation of the gods in many cultures). Electricity and magnetism were originally considered to be two separate forces. This view changed with

3220-431: The designation with ε has been in common use since the 1950s. The SI unit of permittivity is farad per meter (F/m or F·m ). In electromagnetism , the electric displacement field D represents the distribution of electric charges in a given medium resulting from the presence of an electric field E . This distribution includes charge migration and electric dipole reorientation. Its relation to permittivity in

3290-562: The effects of modern physics , including quantum mechanics and relativity . The theoretical implications of electromagnetism, particularly the requirement that observations remain consistent when viewed from various moving frames of reference ( relativistic electromagnetism ) and the establishment of the speed of light based on properties of the medium of propagation ( permeability and permittivity ), helped inspire Einstein's theory of special relativity in 1905. Quantum electrodynamics (QED) modifies Maxwell's equations to be consistent with

3360-576: The existence of a luminiferous aether through which the light propagates. However, subsequent experimental efforts failed to detect the presence of the aether. After important contributions of Hendrik Lorentz and Henri Poincaré , in 1905, Albert Einstein solved the problem with the introduction of special relativity, which replaced classical kinematics with a new theory of kinematics compatible with classical electromagnetism. (For more information, see History of special relativity .) In addition, relativity theory implies that in moving frames of reference,

3430-435: The existence of self-sustaining electromagnetic waves . Maxwell postulated that such waves make up visible light , which was later shown to be true. Gamma-rays, x-rays, ultraviolet, visible, infrared radiation, microwaves and radio waves were all determined to be electromagnetic radiation differing only in their range of frequencies. In the modern era, scientists continue to refine the theory of electromagnetism to account for

3500-516: The form of quantized , self-propagating oscillatory electromagnetic field disturbances called photons . Different frequencies of oscillation give rise to the different forms of electromagnetic radiation , from radio waves at the lowest frequencies, to visible light at intermediate frequencies, to gamma rays at the highest frequencies. Ørsted was not the only person to examine the relationship between electricity and magnetism. In 1802, Gian Domenico Romagnosi , an Italian legal scholar, deflected

3570-435: The formation and interaction of electromagnetic fields. This process culminated in the 1860s with the discovery of Maxwell's equations , a set of four partial differential equations which provide a complete description of classical electromagnetic fields. Maxwell's equations provided a sound mathematical basis for the relationships between electricity and magnetism that scientists had been exploring for centuries, and predicted

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3640-483: The influence of certain conditions, such as being subject to gravity . These simulations are common in cosmology and computational fluid dynamics . N refers to the number of particles considered. As simulations with higher N are more computationally intensive, systems with large numbers of actual particles will often be approximated to a smaller number of particles, and simulation algorithms need to be optimized through various methods . Colloidal particles are

3710-462: The interaction between charged objects. D is related to the charge densities associated with this interaction, while E is related to the forces and potential differences . The vacuum permittivity ε o (also called permittivity of free space or the electric constant ) is the ratio ⁠ D / E ⁠ in free space . It also appears in the Coulomb force constant , Its value

3780-435: The knives took up the nails. On this the whole number was tried, and found to do the same, and that, to such a degree as to take up large nails, packing needles, and other iron things of considerable weight ... E. T. Whittaker suggested in 1910 that this particular event was responsible for lightning to be "credited with the power of magnetizing steel; and it was doubtless this which led Franklin in 1751 to attempt to magnetize

3850-476: The lack of magnetic monopoles , Abraham–Minkowski controversy , the location in space of the electromagnetic field energy, and the mechanism by which some organisms can sense electric and magnetic fields. The Maxwell equations are linear, in that a change in the sources (the charges and currents) results in a proportional change of the fields. Nonlinear dynamics can occur when electromagnetic fields couple to matter that follows nonlinear dynamical laws. This

3920-433: The material. In electrostatics , the permittivity plays an important role in determining the capacitance of a capacitor . In the simplest case, the electric displacement field D resulting from an applied electric field E is More generally, the permittivity is a thermodynamic function of state . It can depend on the frequency , magnitude , and direction of the applied field. The SI unit for permittivity

3990-442: The mechanisms behind these phenomena. The Greek philosopher Thales of Miletus discovered around 600 B.C.E. that amber could acquire an electric charge when it was rubbed with cloth, which allowed it to pick up light objects such as pieces of straw. Thales also experimented with the ability of magnetic rocks to attract one other, and hypothesized that this phenomenon might be connected to the attractive power of amber, foreshadowing

4060-427: The molecular scale, including its density, is determined by the balance between the electromagnetic force and the force generated by the exchange of momentum carried by the electrons themselves. In 1600, William Gilbert proposed, in his De Magnete , that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects. Mariners had noticed that lightning strikes had

4130-447: The objects. The effective forces generated by the momentum of electrons' movement is a necessary part of understanding atomic and intermolecular interactions. As electrons move between interacting atoms, they carry momentum with them. As a collection of electrons becomes more confined, their minimum momentum necessarily increases due to the Pauli exclusion principle . The behavior of matter at

4200-496: The plates of a spherical capacitor. In general, a material cannot polarize instantaneously in response to an applied field, and so the more general formulation as a function of time is That is, the polarization is a convolution of the electric field at previous times with time-dependent susceptibility given by χ (Δ t ) . The upper limit of this integral can be extended to infinity as well if one defines χ (Δ t ) = 0 for Δ t < 0 . An instantaneous response would correspond to

4270-407: The publication of James Clerk Maxwell 's 1873 A Treatise on Electricity and Magnetism in which the interactions of positive and negative charges were shown to be mediated by one force. There are four main effects resulting from these interactions, all of which have been clearly demonstrated by experiments: In April 1820, Hans Christian Ørsted observed that an electrical current in a wire caused

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4340-410: The relative permittivity by ε o : where χ (frequently written χ e ) is the electric susceptibility of the material. The susceptibility is defined as the constant of proportionality (which may be a tensor ) relating an electric field E to the induced dielectric polarization density P such that where ε o is the electric permittivity of free space . The susceptibility of

4410-405: The result was irrational (because the fraction contained π ). In contrast, the ampere was a measured quantity before 2019, but since then the ampere is now exactly defined and it is μ o that is an experimentally measured quantity (with consequent uncertainty) and therefore so is the new 2019 definition of ε o ( c remains exactly defined before and since 2019). The linear permittivity of

4480-466: The same charge, while magnetism is an interaction that occurs between charged particles in relative motion. These two forces are described in terms of electromagnetic fields. Macroscopic charged objects are described in terms of Coulomb's law for electricity and Ampère's force law for magnetism; the Lorentz force describes microscopic charged particles. The electromagnetic force is responsible for many of

4550-438: The subject of interface and colloid science . Suspended solids may be held in a liquid, while solid or liquid particles suspended in a gas together form an aerosol . Particles may also be suspended in the form of atmospheric particulate matter , which may constitute air pollution . Larger particles can similarly form marine debris or space debris . A conglomeration of discrete solid, macroscopic particles may be described as

4620-446: The surface area of a sphere is   4 π r 2   , {\displaystyle \ 4\pi r^{2}\ ,} the electric field a distance r {\displaystyle r} away from a uniform, spherical charge arrangement is This formula applies to the electric field due to a point charge, outside of a conducting sphere or shell, outside of a uniformly charged insulating sphere, or between

4690-431: The very simple case of linear, homogeneous, isotropic materials with "instantaneous" response to changes in electric field is: where the permittivity ε is a scalar . If the medium is anisotropic , the permittivity is a second rank tensor . In general, permittivity is not a constant, as it can vary with the position in the medium, the frequency of the field applied, humidity, temperature, and other parameters. In

4760-532: The world , only a very small number of these exist, such as leptons , quarks , and gluons . However it is possible that some of these might be composite particles after all , and merely appear to be elementary for the moment. While composite particles can very often be considered point-like , elementary particles are truly punctual . Both elementary (such as muons ) and composite particles (such as uranium nuclei ), are known to undergo particle decay . Those that do not are called stable particles, such as

4830-404: Was an electromagnetic wave propagating in the luminiferous ether . In classical electromagnetism, the behavior of the electromagnetic field is described by a set of equations known as Maxwell's equations , and the electromagnetic force is given by the Lorentz force law . One of the peculiarities of classical electromagnetism is that it is difficult to reconcile with classical mechanics , but it

4900-469: Was reported by a Dr. Cookson. The account stated: A tradesman at Wakefield in Yorkshire, having put up a great number of knives and forks in a large box ... and having placed the box in the corner of a large room, there happened a sudden storm of thunder, lightning, &c. ... The owner emptying the box on a counter where some nails lay, the persons who took up the knives, that lay on the nails, observed that

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